The Skew Mean Curvature Flow (SMCF), which naturally generalizes the famous vortex filament equation and describes the evolution of a codimension two submanifold along its binormal direction, is a Schrödinger-type quasi-linear PDE system.

In this talk, I will first introduce the background and recent progresses on SMCF, and then show the local well-posedness of the SMCF in Euclidean spaces of general dimensions.